MinT - Best Known (210−49, 210, s)-Nets in Base 3

Best Known (210−49, 210, s)-Nets in Base 3

(210−49, 210, 464)-Net over F₃ — Constructive and digital

Digital (161, 210, 464)-net over F₃, using

2 times m-reduction [i] based on digital (161, 212, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 53, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(210−49, 210, 1170)-Net over F₃ — Digital

Digital (161, 210, 1170)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−49, 210, 70003)-Net in Base 3 — Upper bound on s

There is no (161, 210, 70004)-net in base 3, because

1 times m-reduction [i] would yield (161, 209, 70004)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5229 506025 475598 145990 798365 867537 011088 959643 673433 710318 831829 530042 123162 873630 475992 412606 847553 > 3²⁰⁹ [i]